Point-occurrence self-similarity in crackling-noise systems and in other complex systems - Condensed Matter > Statistical MechanicsReportar como inadecuado




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Abstract: It has been recently found that a number of systems displaying cracklingnoise also show a remarkable behavior regarding the temporal occurrence ofsuccessive events versus their size: a scaling law for the probabilitydistributions of waiting times as a function of a minimum size is fulfilled,signaling the existence on those systems of self-similarity in time-size. Thisproperty is also present in some non-crackling systems. Here, the uncommoncharacter of the scaling law is illustrated with simple marked renewalprocesses, built by definition with no correlations. Whereas processes with afinite mean waiting time do not fulfill a scaling law in general and tendtowards a Poisson process in the limit of very high sizes, processes without afinite mean tend to another class of distributions, characterized by doublepower-law waiting-time densities. This is somehow reminiscent of thegeneralized central limit theorem. A model with short-range correlations is notable to escape from the attraction of those limit distributions. A discussionon open problems in the modeling of these properties is provided.



Autor: Alvaro Corral Centre de Recerca Matematica, Barcelona

Fuente: https://arxiv.org/







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